Domain decomposition (DD) techniques in general rely on the idea of splitting a larger domain of interest into smaller partitions or subdomains, which results in coupled Degrees-of-Freedom (DoF) at their common interfaces. Typical applications of DD in Boundary-Value problems (BVP) [1]}, [2]} have been successfully employed to efficiently compute the solution of large, discretized Partial Differential Equations (PDEs) in a scalable manner.
DD techniques for parallel approximation of scattered data have been explored previously with Radial Basis Functions (RBF) [3]}, yielding good scalability and closely recovering the underlying solution profiles. In general, overlapping multiplicative and additive Schwarz [4]} iterative techniques for RBF [5]} have proven successful to tackle large-scale problems. Additionally, the use of restricted variants of additive Schwarz (RAS) method as preconditioners, with Krylov iterative solvers, can yield iterative schemes [6]} with \(O(N)\)  computational complexity, as opposed to the typical \(O(N log(N))\)  complexity with traditional RBF reconstructions [7]}. The extensions of these ideas to B-spline bases exposes a way to fully parallelize traditional, serial MFA computations.
